Figure 1: Screenshot of MATCONT showing the main window, 2D-plot, starter and continuer windows in the case of continuation of an LP-curve with detection of CP, BT and BP's (see table below).

MATCONT and CL_MATCONT are MATLAB numerical continuation packages for the interactive bifurcation analysis of dynamical systems. CL_MATCONT forms the computational core of MATCONT, but can also be used independently as a general-purpose non-interactive continuation toolbox in MATLAB. The software development started in 2000 and the first publications appeared in 2003.

Finally, the continuation of homoclinic orbits (both to hyperbolic saddles and to saddle-nodes) is supported by MATCONT, together with detection of a large number of codimension 2 bifurcations along the homoclinic curves.

Figure 2: The graph of adjacency for equilibrium and limit cycle bifurcations in MATCONT.

Figure 3: The graph of adjacency for homoclinic bifurcations in MATCONT; here * stands for S or U.

Relationships between objects of codimension 0, 1 and 2 computed by MATCONT are presented in these figures, while the symbols and their meaning are summarized in the table below, where the standard terminology is used.

An arrow in the figures from an object of type A to an object of type B means that that object of type B can be detected (either automatically or by inspecting the output) during the computation of a curve of objects of type A. Each object of codimension 0 and 1 can be continued in one or two system parameters, respectively.

In principle, the graphs presented in the figures are connected. Indeed, it is known that curves of codimension 1 homoclinic bifurcations emanate from the BT, ZH, and HH codimension 2 points. The current version of MATCONT fully supports, however, only one such connection: BT to HHS.

Equilibrium- and cycle-related objects and their labels within the GUI